Pinto RD, Sartorelli JC
Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970 Sao Paulo, SP, Brazil.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Jan;61(1):342-7. doi: 10.1103/physreve.61.342.
A sequence of attractors, reconstructed from interdrops time series data of a leaky faucet experiment, is analyzed as a function of the mean dripping rate. We established the presence of a saddle point and its manifolds in the attractors and we explained the dynamical changes in the system using the evolution of the manifolds of the saddle point, as suggested by the orbits traced in first return maps. The sequence starts at a fixed point and evolves to an invariant torus of increasing diameter (a Hopf bifurcation) that pushes the unstable manifold towards the stable one. The torus breaks up and the system shows a chaotic attractor bounded by the unstable manifold of the saddle. With the attractor expansion the unstable manifold becomes tangential to the stable one, giving rise to the sudden disappearance of the chaotic attractor, which is an experimental observation of a so called chaotic blue sky catastrophe.
从漏水水龙头实验的液滴间时间序列数据重建的一系列吸引子，作为平均滴水速率的函数进行了分析。我们确定了吸引子中鞍点及其流形的存在，并根据首次返回映射中追踪的轨道所表明的，利用鞍点流形的演化来解释系统中的动态变化。该序列从一个不动点开始，演变为直径不断增大的不变环面（霍普夫分岔），将不稳定流形推向稳定流形。环面破裂，系统呈现出由鞍点的不稳定流形界定的混沌吸引子。随着吸引子的扩展，不稳定流形与稳定流形相切，导致混沌吸引子突然消失，这是所谓混沌蓝天灾难的一个实验观察结果。
